Create Equations Worksheets Grade 9

1. Ava is designing a triangular garden where the area is 84 square meters. The base is 7 meters more than the height. Write an equation relating the area to the base and height.
2. A scientist is studying bacterial growth in a lab culture. The population P(t) after t hours is modeled by the exponential function P(t) = 500 × 2^(t/3). If the scientist needs the population to reach exactly 4,000 bacteria to begin an experiment, how many hours will it take for the culture to reach this population?
3. Matiu is planning a rectangular vegetable garden. The length of the garden is 6 meters more than twice its width. The total area of the garden is 216 square meters. Write an equation in two variables that represents this situation, then determine the width and length of the garden.

…and 5 more problems

1. Emma is mixing two types of fertilizer for her garden. She needs a total of 21 kilograms of the mixture. Type A costs $7 per kilogram, and Type B costs $11 per kilogram. She has a budget of $187 for the fertilizer. Write a system of equations to represent this situation, then determine how many kilograms of each type she should buy.
2. The sum of two numbers is 24. When the larger number is squared and then decreased by the square of the smaller number, the result is 96. What is the larger number?
3. Matiu is designing a rectangular garden with a path around it. The garden itself has length L meters and width W meters. The path surrounding the garden has a uniform width of 2 meters on all sides. Write an equation for the total area A of the garden plus the path, in terms of L and W.

…and 5 more problems

1. A scientist is modeling bacterial growth in a lab culture. The initial population is 500 bacteria, and it doubles every 3 hours. Write an exponential function P(t) = a * b^t that models the population after t hours, and determine how many bacteria will be present after 9 hours.
2. Liam is designing a rectangular garden with a perimeter of 40 meters. He wants the length to be 4 meters more than twice the width. Write a system of equations to model this situation and solve for the dimensions of the garden.
3. Isabella is designing a rectangular garden with a perimeter of 42 meters. The length is 7 meters more than the width. Write an equation that relates the length (l) and width (w) of the garden.

…and 5 more problems